The electrokinetic or zeta potential describes the charge distribution at the interface of two immiscible phases. The zeta potential is important for the characterisation of the solid/liquid interface. The zeta potential can be calculated at the interface between a macroscopic material surface and a liquid from measurements of the streaming potential and the streaming current. Materials with macroscopic surfaces are to be assigned to test samples of different shape and size. These include samples with a flat surface, fibre samples, granulate and powders with a particle size larger than 1 μm (=1·10−6 m).
For measuring the streaming potential and streaming current, the solid sample can be arranged in a measuring cell in such a manner that a capillary or a capillary system with suitable hydraulic permeability is created. The liquid flow through this capillary (flow channel) creates a pressure difference and an electrical signal, which is measured either as voltage (streaming potential) or current (streaming current). Solids with a flat surface are for example arranged parallel next to one another and a capillary with rectangular cross-sectional area results. Fibre samples and granulate are arranged in the form of a plug for example and the liquid flows through the irregular capillary system created thereby.
The zeta potential is calculated according to the classical equations of Helmholtz and Smoluchowski. The following applies for calculation from measurements of the streaming current Istr:
                    ζ        =                                            d              ⁢                                                          ⁢                              I                str                                                    d              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              p                                ·                      η                          ɛ              ·                              ɛ                0                                              ·                      L            A                                              (                  Equation          ⁢                                          ⁢          1                )            wherein dIstr/dΔp is the streaming current coefficient (change of the streaming current with pressure difference over the length of the flow channel), η is the dynamic viscosity of the liquid, ∈ is the dielectric coefficient of the liquid, ∈0 is the permittivity, L is the length of the flow channel, A is the cross section of the flow channel.
The calculation of the zeta potential takes place from measurements of the streaming potential Ustr according to:
                    ζ        =                                            d              ⁢                                                          ⁢                              U                str                                                    d              ⁢                                                          ⁢              Δ              ⁢                                                          ⁢              p                                ·                      η                          ɛ              ·                              ɛ                0                                              ·          κ                                    (                  Equation          ⁢                                          ⁢          2                )            wherein dUstr/dΔp is the streaming potential coefficient (change of the streaming potential with pressure difference over the length of the flow channel), κ is the electrical conductivity of the liquid.
The relationship between the zeta potential and the streaming current (Equation 1) or streaming potential (Equation 2) only leads to identical results if the solid sample is non-conductive. The identity of the zeta potential values is additionally dependent on the electrolyte concentration. The surface or interfacial conductivity influences the correct determination of the zeta potential according to Equation 2 in particular in the case of low ionic strength (I<0.001 mol/l). The zeta potential of conductive solid surfaces (electronically conductive, for example metals, or ionically conductive, for example porous solids or swellable layers or materials) cannot be determined correctly even at higher ionic strengths (I≥0.001 mol/l) according to Equation 2. These limitations necessitate the measurement of the streaming current instead of the streaming potential and the calculation of the zeta potential according to Equation 1.
The measurement of streaming potential and streaming current takes place for example using measuring electrodes made from different materials and with a different size and construction. Electrodes are subject to the process of polarisation, which can have various causes:
Either electrodes of a first type (for example platinum electrodes) or electrodes of a second type (reversible electrodes, for example silver/silver chloride electrodes) are used. Polarisation effects occur in the case of electrodes of the first type in particular and less markedly in the case of electrodes of the second type.
The electrode polarisation is also dependent on the specific surface of the electrodes. Thus, for example, the surface of platinum electrodes (electrodes of the first type) is enlarged by electrochemical application of a porous platinum layer (platinum black). The surface of the silver chloride layer deposited for example on silver electrodes is likewise porous and thereby reduces the tendency to electrode polarisation.
Electrode polarisation is principally a characteristic of electrolyte concentration (ionic strength). Polarisation effects occur on electrodes of the first type even at low ionic strength of an electrolyte dissolved in water. Depending on the quality (size, quality of the coating) and specific surface, the electrode polarisation also increases considerably for electrodes of the second type above a certain ionic strength.
The tendency to polarisation effects of electrodes has an influence both on the measurement of the streaming current and on the measurement of the streaming potential. The influence on the current measurement is occasionally larger than that on the voltage measurement. For small measurement signals of the streaming potential and streaming current, the electrode polarisation increases the error in the measurement and consequently reduces the quality of the zeta potential calculated according to Equation 1 or Equation 2.
There is a series of commercial measuring devices for measuring the streaming potential, but also the streaming current for determining the zeta potential at macroscopic solid surfaces. In these measuring devices, the effect of the electrode polarisation, described by the difference in the electric potential between the two measuring electrodes in the rest state, is counteracted by corresponding structural measures and measurement protocols.
In the case of a two-point measurement, the voltage value in the rest state (no fluid flow, asymmetry potential U0) and the streaming potential at a constant pressure difference, Ustr(Δp) are used in order to calculate the streaming potential coefficients in Equation 2 as a differential quotient ΔUstr/Δp, where ΔUstr=Ustr(Δp)−U0. This method is suitable for measurement conditions, in which the asymmetry potential U0 results into a small contribution to the measured streaming potential (<10%).
In the case of a pressure stage measurement, the streaming potential Ustr(Δp) is determined at different constant pressure differences and the streaming potential coefficient is calculated in Equation 2 from the linear regression of the measured points Ustr versus Δp. Due to the larger number of measurement points compared to the two-point measurement, the quality of the calculated streaming potential coefficient is improved.
The technical realisation of such methods for determining the streaming potential and streaming current coefficients takes place in commercial measuring devices and provisional measurement apparatus by applying a pressure difference by means of an external pump or gas pressure.
The measurement of the streaming potential and the streaming current according to conventional measuring methods is limited to the determination of the zeta potential at low ionic strengths however.
Further prior art is disclosed in WO 86/00707, Pu et al., “Label-free detection of heparin, streptavidin, and other probes by pulsed streaming potenzials in plastic microfluidic channels”, Anal Chem 2008 Sep. 1; 80(17):65326, Luna-Vera et al., “Adsorption kinetics of proteins in plastic microfluidic channels: Real-time monitoring of lysozyme adsorption by pulsed streaming potenzials”, Biosensors and Bioelectronics 25 (2010) 1539-1543, JPH02216443 and U.S. Pat. No. 6,023,661.